An online activity provides instructional strategies that can help students engage in mathematical modeling and autonomous learning.
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Digital Learning Routes: An Example of Mathematical Modeling
Salomé Martínez, Flavio Guiñez, and Darío González
Composing Tangram Puzzles to Support Shape Transformation
Laura Bofferding and Yi Zhu
Different types of tangram puzzles can encourage students to make sense of problems and engage in the computational thinking practice of debugging.
(Counter)Productive Practices for Using Student Thinking
Laura R. Van Zoest, Shari L. Stockero, Blake E. Peterson, and Keith R. Leatham
Learn why collecting, clarifying, and revoicing—often great teaching moves—do not always work.
Recalibrating Beliefs and Teaching Practices
Amanda L. Cullen
Exploratory Writing to Support Mathematical Sense Making
Madelyn W. Colonnese
A teacher implements this type of personal prose in the classroom to help students make sense of fractions and communicate ideas.
Area of a Changing Triangle: Piecing It Together
Blake Peterson
Examining the covariation of triangle dimensions and area offers a geometric context that makes analyzing a piecewise function easier for students.
Beyond the Sign Rules
Jessica Pierson Bishop, Lisa L. Lamb, Ian Whitacre, Randolph A. Philipp, and Bonnie P. Schappelle
Are your students negative about integers? Help them experience positivity and joy doing integer arithmetic!
Trigonometry and the World Water Crisis
Courtney Fox and Anna DeJarnette
This full unit in trigonometry introduces the world water crisis. Students engage in real-world problem-solving activities that access 21st-century skills while learning mathematics.
The Importance of Play in Middle School Mathematics
Kate Degner
Using question 28 from the May Problems to Ponder in volume 114, the author and her seventh- and eighth-grade students launched into a discussion of creativity, linearity, piecewise, and recursive definitions of functions. This pattern to ponder provided rich mathematical opportunities for all students in my middle school classroom.
Problems to Ponder
Molly Rawding and Steve Ingrassia
Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.
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